Rheological properties of supramolecular polymers (SMPs) depend on their equilibrium structure including the size, the number, and the topology of aggregates. A polymer with a hydrogen bonding (H-bonding) motif at both ends is one widely used precursor to build SMPs. Due to the complex interplay between chain stiffness, H-bonding interaction, polarity along a chain, and polymer conformational entropy, it is difficult to theoretically predict the structure of SMPs. In this work we investigate thermodynamics of SMPs with H-bonding ends in a wide range of densities. A replica exchange stochastic approximation Monte Carlo method with coarse-grained models for polyethylene and polybuthylene glycols is used. Our simulation shows that SMPs have two morphological transition lines with increasing temperature, a ring-linear transition, and a linear-free chain transition. The latter is a thermodynamic transition and turns out to be continuous. Comparing the two different spacers, we find that ring-linear transition temperatures differ from each other at the constant volume fraction due to different looping probabilities, which can be calculated from the average polymer size by mean field. However, the linear-free chain transition temperatures are similar because the entropic penalty to form a hydrogen bond mainly depends on the probability of finding H-bonding groups in a system, which is the same for both systems at a given volume fraction.